Abstract: A workpiece holding fixture in the form of an elongated cylindrical base member provided with an end adapted for mounting on the end of a rotatable spindle, such as the headstock of a lathe or like machine tool, the cylindrical member being provided at its other end with a seat appropriately arranged to engage a portion of the periphery of a workpiece of irregular shape, such as a pipe elbow or the like, and having clamping means for securely holding the workpiece on the seat with the portion of the workpiece on which a machining or fabricating operation is to be effected disposed rotatable through the intermediary of the holding fixture around an axis of rotation coinciding with the axis of rotation of the holding fixture.